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Common Core Math6th GradeExpressions & Equations

6.EE.5: Check Solutions by Substitution

Also written as 6.EE.B.5 and CCSS.MATH.CONTENT.6.EE.B.5 · Cluster: Reason about and solve one-variable equations and inequalities.

Make a 6.EE.5 WorksheetAll 29 6th Grade Math Standards

The Official Wording

Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

Common Core State Standards, Grade 6, Expressions & Equations · Read it at the source · Checked October 14, 2026

What 6.EE.5 Means in Plain English

Sixth graders treat an equation as a question: which number makes it true? With x + 7 = 12 and candidates 3, 4 and 5, they substitute each. Only 5 + 7 = 12 works. For the inequality 2x < 9, two of the three pass, 3 and 4.

No solving method is required yet, and that is deliberate. The standard builds the meaning of “solution” before 6.EE.7 teaches the one-step moves and 6.EE.8 shows infinitely many solutions on a number line. The habit of checking by substitution pays off again with two-step equations in 7.EE.4.

6.EE.5 I Can Statements

  • I can substitute a number into an equation to see if it is true.
  • I can find which numbers in a set make an inequality true.
  • I can explain what it means for a number to be a solution.

6.EE.5 Worked Example

A set of four candidates, one equation, and a plain yes or no for each after substituting.

Problem

Which number from the set {2, 4, 6, 8}, if any, makes 3x + 2 = 14 true?

Which value from {2, 4, 6, 8} solves 3x + 2 = 14?
  1. A solution is a number that makes the two sides equal. Test the candidates one at a time, starting with 2.3(2) + 2 = 8, and 8 ≠ 14
  2. Try 4. Multiply first, then add.3(4) + 2 = 14, true
  3. Keep going. The question asks about the whole set, and a set could hold more than one solution or none at all.3(6) + 2 = 20, and 3(8) + 2 = 26
  4. Only one candidate made a true statement.x = 4
AnswerOnly 4 from the set is a solution

Check it: Read the true statement back: 3 × 4 is 12, plus 2 is 14, the number on the other side. The other three gave 8, 20 and 26, none of them 14.

Common Mistakes with 6.EE.5

Stopping at the first hit

x² = 2x with {0, 2, 5}: “0 works, so the answer is 0”

Try this: Test every number in the set before answering. Here 2 works too (4 = 4), so the solution set is {0, 2}.

Substituting into one side only

For 2x + 1 = x + 7, test x = 3: 2(3) + 1 = 7, “so 3 works”

Try this: Evaluate both sides separately and compare: left side 7, right side 3 + 7 = 10. Not equal, so 3 is not a solution.

Treating the inequality like an equation

x + 3 < 10 with {5, 7, 9}: “only 7 makes it 10, so 7”

Try this: Ask whether each statement is true as written: 8 < 10 yes, 10 < 10 no, 12 < 10 no. Only 5 is a solution.

Where 6.EE.5 Fits

Comes Before5.OA.1Evaluate numerical expressions with grouping symbols.6.EE.2Evaluate an expression at a given value of its variable.
Alongside6.EE.6Use a variable for an unknown number in a real problem.6.EE.4Decide whether two expressions name the same number for every value.
Comes Next6.EE.7Solve x + p = q and px = q instead of testing candidates.6.EE.8Write x > c or x < c and show its infinitely many solutions on a number line.7.EE.4Solve two-step equations and inequalities and check the solution.

Practice 6.EE.5

Math Worksheet GeneratorFree Tool“Is it a solution?” pages: an equation or inequality, a short set of candidates, and a yes or no to justify by substituting.Check solutionsInequalitiesAnswer key
Make a Worksheet

Quick Check

  1. Is 9 a solution of 27 ÷ x = 3?
  2. Which numbers from {1, 3, 5, 7} make 4x - 2 < 15 true?
  3. Which number from {2, 3, 4} makes 5n + 4 = 19 true?

6.EE.5: Other Names

6.EE.56.EE.B.5CCSS.MATH.CONTENT.6.EE.B.5

Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Official wording from the Common Core State Standards PDFs at corestandards.org, last checked October 14, 2026. The explanation, I can statements, example, mistakes and practice on this page are EMStudio’s own, written beside the official wording. They are not part of the standard.